Prosecutors in Manhattan have decided not to retry Steven H. Davis, the former chairman of Dewey & LeBoeuf, the once-prominent New York law firm that collapsed in bankruptcy in 2012, a person briefed on the matter said on Friday.

Two other former executives of Dewey are expected to be headed to a new trial on charges they oversaw an accounting fraud at the firm.

The criminal trial of Mr. Davis and the two other former Dewey executives — Stephen DiCarmine and Joel Sanders — ended in a mistrial in October.

On Friday, a prosecutor working for Cyrus R. Vance Jr., the Manhattan district attorney, said the office intended to conduct a new trial when a jury was unable to reach a verdict on 93 charges against the three men after 21 days of deliberation. The trial judge declared a deadlock in the proceeding after the jury earlier acquitted the men on 58 charges.

But in speaking before Justice Robert M. Stolz of the New York Supreme Court in Manhattan, the prosecutor, Peirce Moser, was unclear on whether Mr. Vance intended to retry all three defendants, or just some of them.

Mr. Moser declined to elaborate on his comment about a new trial when he was asked about it after the brief court appearance. A spokeswoman for Mr. Vance also declined to comment further.

Mr. Moser and lawyers for the three defendants are scheduled to be in court on Monday, when it is expected that Mr. Vance’s office will make clear its intentions on retrying any of the defendants.

Over the last several weeks, the lawyers for Mr. Davis, Mr. DiCarmine and Mr. Sanders have had meetings with top prosecutors to argue why their clients should not be retried. Mr. Vance has attended some of those meetings.

Prosecutors are considering dismissing the charges against Mr. Davis by offering him a deferred prosecution agreement that would require him to refrain from any improper conduct for a period of time, said another person briefed on the matter.

Such an agreement would be unusual given that Mr. Davis was already indicted on dozens of criminal charges and tried once by a jury. But the deal, if approved, would enable prosecutors to avoid retrying Mr. Davis without dismissing the charges outright.

The first trial of the three men began at the end of May and concluded with a hung jury in October.

In interviews conducted after the trial, jurors told reporters and the lawyers involved in the case that prosecutors presented too many charges against the defendants and the case was too complex. The jurors also gave different views on the relative culpability of the three defendants.

Mr. Moser, who led the prosecution in the first trial, appeared before Justice Stolz on Friday to discuss the timing of a trial for a fourth defendant, Zachary Warren, a low-level employee at Dewey who was also indicted but not tried with the law firm’s three former executives.

Mr. Moser told the judge that Mr. Warren should be tried after any retrial of the former executives. Mr. Warren’s lawyer, Paul Shechtman, said it would be unfair to make Mr. Warren, currently working as a lawyer for a small firm in Pittsburgh, wait that long for a trial on the charges against him.

Justice Stolz seemed to sympathize with Mr. Warren’s plight. He told Mr. Moser that if Mr. Warren’s trial were conducted first, it would not pose much legal danger to any retrial.

“There aren’t too many secrets in this case,” the judge said.

The judge, however, put off making any decision on the timing of trials until the conference on Monday, during which lawyers for all of the defendants, including Mr. Warren, will be present.

Justice Stolz must still decide motions filed by the defense lawyer for the former executives to dismiss the charges the jury could not reach a verdict on.

The former executives are still facing dozens of counts of grand larceny, falsifying business records and scheming to defraud.

Ben Protess contributed reporting.

A version of this article appears in print on , on Page B3 of the New York edition with the headline: New Fraud Trial Expected for 2 of 3 Former Dewey Executives. Order Reprints | Today’s Paper | Subscribe